Finding specific heat of an object graphically

[armolinasf]

Homework Statement

Samples A and B are at different initial temperatures when they are placed in a thermally isolated container and allowed to come to thermal equilibrium. Figure a gives their temperatures T versus time t. Sample A has a mass of 5.2 kg; sample B has a mass of 1.6 kg. Figure b is a general plot about the material of sample B. It shows the temperature change T that the material undergoes when energy is transferred to it as heat Q. The change T is plotted versus the energy Q per unit mass of the material.

The Attempt at a Solution

The heat gained by object b must equal the total heat of object a. So Qb=Qa=Q/mb*mb, mb=mass of object b.

but Q=mcΔt ==> c=Q/mΔt would Δt then just be the total change from 100 to 60 degrees?

this would give me 25600/(5.2*60)=82.05 which is incorrect. Where Am I going wrong?

Thanks for the help

 

[grzz]

The heat gained by object b must equal the total heat of object a.

I think it is better to replace the underlined by 'heat lost by'.

 

[grzz]

but Q=mcΔt ==> c=Q/mΔt would Δt then just be the total change from 100 to 60 degrees?

I think that you mean that [itex]\Delta[/itex]T is the change from 100 to 40, i.e. 60deg because we are considering A.

 

[grzz]

So Qb=Qa=Q/mb*mb, mb=mass of object b.

Can the poster explain what the above mean?

 

[asteriatic]

and clarification

I would like to commend you on your attempt at finding the specific heat of object B using graphical data. However, there are a few points that need clarification and correction.

Firstly, the heat gained by object B may not necessarily equal the total heat of object A. Heat is not a conserved quantity, as it can be lost or gained by an object through various processes such as conduction, convection, and radiation. Therefore, it is important to consider the specific conditions of the experiment and the materials involved before assuming that the heat gained by object B is equal to the total heat of object A.

Secondly, your equation to calculate the specific heat (c) is correct, but the value for Q should be the heat gained by object B, not the total heat. This means that you should use the value for Qb in your calculation, not Q.

Lastly, the value for Δt should be the time it takes for object B to change from its initial temperature to its final temperature, not the total change in temperature. This is because specific heat is a measure of how much heat is required to change the temperature of an object by a certain amount, not the total temperature change.

I would suggest reviewing your calculations and making sure to use the correct values for Q and Δt. Additionally, it may be helpful to double check the units of your final answer to ensure that they are in agreement with the units of specific heat (J/kg*K).

I hope this helps and good luck with your homework! Remember, as a scientist, it is important to always double check your calculations and assumptions to ensure accuracy and precision in your results.